Precalculus Examples

$g (x) = 4 x^{3}$

Find $f (- x)$ .

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Find $g (- x)$ by substituting $- x$ for all occurrence of $x$ in $g (x)$ .

$g (- x) = 4 {(- x)}^{3}$

Apply the product rule to $- x$ .

$g (- x) = 4 ({(- 1)}^{3} x^{3})$

Raise $- 1$ to the power of $3$ .

$g (- x) = 4 (- x^{3})$

Multiply $- 1$ by $4$ .

$g (- x) = - 4 x^{3}$

A function is even if $f (- x) = f (x)$ .

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Check if $f (- x) = f (x)$ .

$- 4 x^{3}$ $\neq$ $4 x^{3}$

Since $- 4 x^{3}$ $\neq$ $4 x^{3}$ , the function is not even.

The function is not even

A function is odd if $f (- x) = - f (x)$ .

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Multiply $4$ by $- 1$ .

$- f (x) = - 4 x^{3}$

Since $- 4 x^{3} = - 4 x^{3}$ , the function is odd.

The function is odd